Question

Which is an equation of the given line in standard form?

A. -6x+5y=13
B. -6x+7y=-11
C. -6x+7y=11
D. -7x+6y=-11

Answer 1

The slope:
`m=(y_2-y_1)/(x_2-x_1)`

The coordinates of the points:

`(-3;\ -1)\to x_1=-3;\ y_1=-1;\ \left((1)/(2);\ 2\right)\to x_2=(1)/(2);\ y_2=2`

Substitute:
`m=(2-(-1))/((1)/(2)-(-3))=(3)/(3(1)/(2))=(3)/((7)/(2))=3\cdot(2)/(7)=(6)/(7)`

We have:
`y=(6)/(7)x+b`

Substitute the coordinates of the point (-3; -1) to the equation of the line:


`-1=(6)/(7)\cdot(-3)+b\\\\-1=-(18)/(7)+b\ \ \ |+(18)/(7)\\\\b=(11)/(7)`

Therefore we have:

`y=(6)/(7)x+(11)/(7)\ \ \ |\cdot7\\\\7y=6x+11\ \ \ |-6x\\\\\boxed{-6x+7y=11}`

Answer: C. -6x + 7y = 11